Compressed Sensing via Sequential Majorization-Minimization and Collaborative Neurodynamic Optimization.

Abstract

Compressed sensing formulations that target an $\ell _{0}$ -norm objective are inherently nonconvex and discontinuous. In this article, a global optimization problem with a power-mean function is first formulated for compressed sensing. To mitigate the numerical instability of minimizing the power-mean function with a large negative exponent, the problem is reformulated as a sequential majorization-minimization (MM) problem with iteratively reweighted convex surrogate functions at different anchor points. To eliminate the dependency of the solution quality on anchor points, multiple neurodynamic optimization models are employed to seek global optimal solutions collaboratively through repeated reinitialization using a particle swarm optimization rule. Extensive experiments demonstrate that the proposed method achieves superior performance compared to 14 state-of-the-art algorithms in terms of signal sparsity and reconstruction accuracy.